EDA with R: Red Wine Quality Dataset

by Benjamin Soukiassian

Exploratory Data Analysis with R on a Red Wine quality dataset.

Part of the Data Analysis Nanodegree by Udacity.

1.Exploration

Univariate Analysis

Let’s load our csv file and have a look at the dimension of the dataset

library(ggplot2)
wine <- read.csv('wineQualityReds.csv')
dim(wine)
## [1] 1599   13

We have 1599 observations of 13 variables. Let’s now have a look at the structure and variables types of the dataset.

str(wine)
## 'data.frame':    1599 obs. of  13 variables:
##  $ X                   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

All of the relevant variables are numerical except the quality variable which are integers. By looking at the dataset reference file, we learn that the quality score is graded within a 0 to 10 interval. We can deduce that quality score is a discrete variable, given its integer type.

Let’s take a look at the summary of the data for the quality variable.

summary(wine$quality)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.636   6.000   8.000

Our min quality score is 3 while our max is 8, which is a bit suprising given the 1 to 10 interval. we have a mean of 5.636 and median at 6.

Let take a look at a box plot:

ggplot(aes(x="Wine", y = quality), data = wine) +
  geom_boxplot() +
  stat_summary(fun.y = mean, geom = "point", shape = 4)

50% of the bottles are graded between 5 and 6, which considering the 1 to 10 scale seem quite concentrated. We have a few outliers at 3 and 8 (min and max values) but most of the values fall between 4 and 7.

To get a better sense of this concentration Let’s plot the data as a histogram of frequencies.

ggplot(aes(x=quality), data=wine) + 
  geom_histogram(binwidth = 0.5) +
  scale_x_continuous(breaks = seq(1,10,1)) +
  scale_y_continuous(breaks = seq(0, 650, 50))

The frequency distribution is indeed concentrated around 5 and 6. It also appear to be a little skewed toward the right (upper quality).

The obvious interesting question regarding this dataset is going to be to try to find which variables are correlated with the quality notation. This question imply the assumption that this notation is trustworthy.

Let’s go back to our dataset attributes.

str(wine)
## 'data.frame':    1599 obs. of  13 variables:
##  $ X                   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

The dataset provides us with a number of chemical elements which were obtained through physicochemical tests. We have for instance the percent of alcohol, the density, the pH or different measures of acidity.

Let’s create a correlation matrix to get a sense of which attributes are worth exploring further.

library(corrplot)
m <- cor(wine[,1:13]) # remove quality.factor & quality.group
corrplot(m, method="number", type="lower",
         tl.col='black', tl.cex=1, 
         tl.srt=40)

Thanks to the correlation matrix, we are able to get a sense of the relationship between each pair of variables.

One of the first thing that visually jumps out is that there do not seem to have any “very strong” relationship between pairs of variables. But a few pairs appear to have interesting relationships nonetheless. For instance, we see that citric.acid appear to have a positive relationship with fixed.acidity, with a correlation coefficient of 0.672 (Strong relationship). However, citric.acid seems to have a negative relationship with volatile acidity. Corr: -0.552 (Moderate).

We also see that pH has a negative relationship with both fixed.acidity (-0.68) and citric.acid (-0.54) which makes sense because a low pH means more acidity.

But let’s focus on the plots between the different chemical attributes and quality. First, by looking at the correlation coefficients at the bottom of the plot, we see that alcohol is the attribute most correlated with quality, (which I must admit I find quite surprising). The second is volatile acidity with a negative correlation of -0.39, and Sulphates is the third.

Let’s take a deeper look at each of these three variables separately, and then we’ll look at the relationship between those variables and quality.

Alcohol

library(gridExtra)
create_box_and_hist_plots <- function(variable, data, label, binwidth = 0.1) {
  plot1 <- ggplot(aes(x="Wine", y=variable), data = data) +
    labs(y=label) +
    geom_boxplot() +
    stat_summary(fun.y = mean, geom = "point", shape = 4)
  
  plot2 <- ggplot(aes(variable), data=data) +
    geom_histogram(binwidth = binwidth) +
    labs(x=label)
  return(
    grid.arrange(plot1, plot2, ncol=2)
  )
}

create_box_and_hist_plots(wine$alcohol, wine, 'Wine', 0.1)

Mode <- function(x) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}
Mode(wine$alcohol)
## [1] 9.5
summary(wine$alcohol)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.40    9.50   10.20   10.42   11.10   14.90

We can see that the distribution of alcohol % among the wines is positively skewed and has a few upper outliers. The median % is 10.20, mean 10.42 and the IQR is 1.6 the mode is 9.5.

Volatile Acidity

create_box_and_hist_plots(wine$volatile.acidity, wine, 'Volatile Acidity', 0.02)

summary(wine$volatile.acidity)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1200  0.3900  0.5200  0.5278  0.6400  1.5800

The distribution of volatile acidity is positively skewed. The median value is 0.52 and the mean ~0.53, with an IQR of 0.26.

Sulphates

create_box_and_hist_plots(wine$sulphates, wine, 'Sulphates', 0.02)

summary(wine$sulphates)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3300  0.5500  0.6200  0.6581  0.7300  2.0000

The sulphate distribution has much more outliers than the previous ones we saw. It is still positively skewed. It has a mean of 0.62, a median of 0.66 and an IQR of 0.18.

Bivariate Analysis

Alcohol

Let’s start by plotting percent of alcohol against quality.

ggplot(aes(quality, alcohol), data = wine) +
  geom_point()

It is quite hard to see anything with the discrete quality data. Let’s add some noise to the data with jitter.

ggplot(aes(quality, alcohol), data = wine) + 
  geom_jitter(alpha=1/2, width = 1.8, height = 0.2)

There could be a light positive relationship but it’s still hard to grasp. Let’s add a mean line.

ggplot(aes(quality, alcohol), data = wine) + 
  geom_jitter(alpha=1/2,  width = 1.8, height = 0.2) +
  stat_summary(fun.y = mean, color="orange", geom="line", size = 1)

The mean variable shows a positive relationship, but by looking at the raw data the relationship do not seem very strong.

cor.test(wine$quality, wine$alcohol, method="pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  wine$quality and wine$alcohol
## t = 21.639, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4373540 0.5132081
## sample estimates:
##       cor 
## 0.4761663

The correlation coefficient is 0.4762, that is consistent with what we saw on the correlation matrix. Using the guide that Evans (1996) suggest for different r intervals this value is considered to be moderate.

So the percent of alcohol is moderately correlated to quality, but it probably does not alone account for the total variation in wine quality. Thankfully, we still have other attributes to look at.

Volatile acidity

Volatile acidity (VA) is a measure of the wine’s volatile (or gaseous) acids. The primary volatile acid in wine is acetic acid, which is also the primary acid associated with the smell and taste of vinegar. So it is is generally considered to be a spoilage product but apparently some winemakers seek a low or barely detectible level to add to the perceived complexity of a wine

ggplot(aes(quality, volatile.acidity), data = wine) +
  geom_jitter(alpha=1/2, width = 2) +
  stat_summary(fun.y=mean, colour="orange", geom="line", size = 1)

We can definitely see a negative relationship between the variables, but as with alcohol, it does not seem really strong.

cor.test(wine$quality, wine$volatile.acidity, method="pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  wine$quality and wine$volatile.acidity
## t = -16.954, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.4313210 -0.3482032
## sample estimates:
##        cor 
## -0.3905578

And indeed the -0.39 Pearson Correlation coefficient is considered weak, nearly moderate.

Sulphates

Sulphates is the third variable most correlated with quality.

ggplot(aes(quality, sulphates), data=wine) +
    geom_jitter(alpha=1/2, width = 2) +
    stat_summary(fun.y=mean, colour="orange", geom="line", size = 1)

We can see a very light positive relationship between sulphates and quality, relationship confirmed by the correlation coefficient of 0.251.

Multivariate Analysis

Since alcohol and volatile acidity are still the variables with the biggest relationship to quality, let’s try to plot them againts each other while adding quality as a third variable.

wine$quality.factor <- as.factor(wine$quality)
ggplot(aes(alcohol, volatile.acidity), data = wine) +
  geom_point(aes(color=quality.factor)) +
  scale_colour_brewer("Quality", palette="RdBu")

The best wines appear to be mostly located in the lower right of the plot and the worst higher on the left. But there are so many middle range wine with quite a important dispersion that it’s hard to see clearly the wines graded higher or lower on the quality scale.

Let’s divide our quality notation data into three groups: Low, Medium and High and plot only the Low and High groups.

wine$quality.group <- cut(wine$quality,  breaks=c(3,4,6,8),
                           labels=c("Low","Medium","High"),
                           include.lowest=TRUE)

low_high_wines <- subset(wine, quality.group %in% c('Low','High'))

ggplot(aes(alcohol, volatile.acidity), 
       data = low_high_wines) +
  geom_point(aes(color=quality.group)) +
  scale_colour_brewer(palette="Set1")

The difference is much more visible but the two data groups are clearly overlapping.

Let’s plot sulphates against alcohol and color by quality group, using our low_high_wines subset.

ggplot(aes(sulphates, alcohol), data=low_high_wines) +
  coord_cartesian(xlim=c(0.3, 1.5)) +
  geom_point(aes(color=quality.group)) +
  scale_colour_brewer(palette="Set1")

Again, our groups are overlapping.

Let’s try something else by plotting a 3D scatterplot with the three variables studied so far (volatile.acidity, sulphates, alcohol).

library(scatterplot3d)
attach(low_high_wines)
scatterplot3d(volatile.acidity, sulphates, alcohol, 
              angle=120, color=as.numeric(quality.group))

While we can’t seem to avoid some overlapping, the two clusters are definitely visible.

Bonus

Althought in practice it doesn’t make much sense since the data is already labelled and overlapping, I wonder how an unsupervised clustering algorithm like K-mean would cluster the Low-High data.

m = as.matrix(cbind(low_high_wines$alcohol, low_high_wines$volatile.acidity), ncol=2)

cl=(kmeans(m, 2, iter.max=1, nstart=1))
low_high_wines$cluster=factor(cl$cluster)
centers=as.data.frame(cl$centers)

ggplot(data=low_high_wines, aes(alcohol, volatile.acidity)) + 
 geom_point(aes(color=cluster)) +
 scale_colour_brewer(palette="Set1") +
 geom_point(data=centers, aes(x=V1,y=V2, color="Center")) +
 geom_point(data=centers, aes(x=V1,y=V2, color="Center"), size=22, alpha=.1,
            show.legend = FALSE)

It splits the data vertically at about 11.5% on the alcohol scale.

2.Final plots

Alcohol vs Quality

ggplot(aes(quality, alcohol), data = wine) +
  geom_jitter(alpha=1/2,  width = 1.8, height = 0.2, color="#008cff") +
  coord_cartesian(xlim=c(3, 8)) +
  scale_y_continuous(breaks=seq(8,15,1)) +
  stat_summary(fun.y = mean, aes(shape="mean", color="mean"), geom="line", size = 1) +
  geom_path(stat = "summary", fun.y = quantile, 
            fun.args=list(probs=.25), linetype=1, aes(color="quartiles") )+
  geom_path(stat = "summary", fun.y = quantile, 
            fun.args=list(probs=.5), linetype=2, aes(color="median"), size = 1)+
  geom_path(stat = "summary", fun.y = quantile, 
            fun.args=list(probs=.75), linetype=1, color="#e03aea") +
  scale_colour_manual("Legend", values=c("mean"="orange", "median"="#ff3098", "quartiles"="#e03aea")) +
  labs(x="Quality Grade", y="Alcohol (%)", title="Alcohol vs Quality")

This plot shows the relationship between Alcohol and quality grade. While the raw data is quite dispersed, we are able by to assert the positive nature of the relationship by plotting mean, median and quartiles lines.

Volatile Acidity vs Alcohol

ggplot(aes(alcohol, volatile.acidity), data = low_high_wines) +
  geom_point(aes(color=quality.group)) +
  coord_cartesian(ylim=c(0, 1.2)) +
  labs(x="Alcohol (%)", 
       y="Volatile Acidity (g /cubic decimeter) ", 
       title="Volatile Acidity vs Alcohol,
       colored by Quality",
       colour="Quality Group") +
  scale_colour_brewer(palette="Set1")

This scatterplot shows the relationship between Alcohol and Volatile acidity while coloring the data points by one of the two “Low” or “High” quality groups. I choosed to plot the two most extremes groups because the medium group has a lot of dispersed data points, making it more difficult to see the underlying distribution. We see on the plot that the “Low” quality wines tend to be higher on the volatile acidity scale than the “High” quality wines, while the “High” quality wines are higher than the “Low”" on the alcohol scale. The two groups are overlapping.

3D Scatterplot (Volatile Acidity, Sulphates, Alcohol)

attach(low_high_wines)
scatterplot3d(volatile.acidity, sulphates, alcohol, pch = 19,
              main = "3D Scatterplot (Volatile Acidity, Sulphates, Alcohol)", 
              color = (22.7*as.numeric(quality.group)), box = FALSE, 
              cex.lab   = 1.2, cex.symbols=0.7, angle=120)

Legend: blue: High Quality pink: Low Quality

This scatterplot is a 3D representation of the relationship between alcohol, sulphates and volatile acidity for the “Low-High” data points. The motivation for the plot is to try to see if we are able to get natural clusters of the two extremes quality groups by plotting the 3 most influencial variables for quality. We are indeed able to see clusters but they are still overlapping.

3.Reflection

We’ve seen that a few chemical elements have relationships with wine quality but haven’t found any strong correlation. All of our modelling is based on the assumption the quality notation is trustworthy that there is a direct relationship between the grades and the physicochemical properties.

Regarding the dataset, I found the information gap between the accucary of physicochemical data and the quality scale (graded on a discrete scale from 1 to 10, in practice only from 3 to 8) to be too important. I wished the experts who graded the wines had given more variables to study: e.g. perceived acidity, color..

Even if accurately graded, “Quality” is quite an abstract concept. Are we talking about quality against some sort of standard ? Given that wines differ from region to region and all of our dataset wines are coming from Portugal, are we talking about the quality for a Portuguese wine of that region, or of quality for all red wines?

On a regional scale and If our assumptions are true, we may have missed relationships that more complex modeling techniques could put forward. But I do have concerns regarding a theorical global wine grading using physicochemical data, it seems that people who buy Bordeaux are probably not looking for the same experience as people buying Argentine wine. A great argentine wine taste different than a great Bordeaux. So even assuming that it is possible to accurately represent quality or taste through physicochemical data, it seems likely that what is considered “great” could differ in physicochemical terms depending on the region.